Gravitational instability of the inner static region of a Reissner-Nordström black hole

G. DOTTI Y R. GLEISER

CLASSICAL AND QUANTUM GRAVITY

IOP PUBLISHING LTD

Año: 2010 vol. 27 p. 185007 - 185007

0264-9381

Reissner--Nordström black holes have two static regions: $r > o$ and $0 < r < i$, where $ i$ and  $ o$ are the inner and outer horizon radii. The stability of the exterior static region has been established long time ago. In this work we prove that the interiorstatic  region is unstable under linear gravitational perturbations, by showing that  field perturbations compactly supported within this regionwill generically excite a mode that grows exponentially in time.This result gives an alternative reason to mass inflationto consider the space time extension beyond the Cauchy horizon as physically irrelevant,and thus provides support to the strong cosmic censorship conjecture, which is also backed  by recent evidence of a  linear gravitational instability in the interior region of Kerr black holes found by the authors.The use of intertwiners to solve for the evolution of initial data plays a key role, and adapts without change to the case of super-extremal n black holes, allowing to completethe proof of the linear instability of this naked singularity. A particular intertwineris found such that the intertwined Zerilli field has a geometrical meaning -it is  the first order variation of a particular Riemann tensor invariant-. Using this, calculations can be carried out explicitely for every harmonic number.